Quiz 6 Review

Part b asked for a CI for the slope \(\beta_1\). For this one you use the formula \(\hat{\beta_1} \pm t^{\ast}_{n-p-1} SE(\hat{\beta_1})\). \(n\) is the sample size and \(p\) is the number of predictors (1 in this case).

You get the \(\hat{\beta_1}\) and \(SE(\hat{\beta_1})\) from a computer or calculator and lookup the \(t^{\ast}\) in the table. Remember to round the degrees of freedom down when looking up \(t^{\ast}\) in the table. We want to be conservative and not overstate our sample size.

Part d asked for a different kind of interval, one for a \(\hat{y}\).

For this kind of problem, you'll use either \(\hat{y} \pm t^{\ast} SE_{\hat{\mu}}\) or \(\hat{y} \pm t^{\ast} SE_{\hat{y}}\), depending on whether you are predicting for all observations with that value of \(X\) or for a single observation.

We don't give you the formulas for the \(SE_{\hat{\mu}}\) or \(SE_{\hat{y}}\). Minitab gives the \(SE_{\hat{\mu}}\) (they call it SE-Fit). So in practice you'll just take the CI or PI from the Minitab output.

If you're struggling with the Minitab or stats part of this stuff, let me know. Send me an email thomas-augspurger@uiowa.edu or stop by my office hours: Tuesdays from 10:30 - 11:30 and 12:30 - 1:30 (or by appointment). I want you to be comfortable with the basics of regression; the rest of the course builds on what we did last week.